Question

Item 11

The double box-and-whisker plot shows the goals scored per game by two soccer teams during a 25 game season.


Express the difference in the measures of center as a multiple of the measure of variation.




The difference in the medians is

times the IQR.

Answer 1

The difference in medians, 4, is (4/3) or 1.3333 times the IQR.

Explanation:

The double box and whiskers plot that is missing for the question is obtained online and presented in the attached image to this solution.

The measure of centre for a boxplot is the median and the measure of variation is the interquartile range.

The median is denoted by the number thay corresponds to the vertical line dividing the boxplot into two parts.

For team A, median = 4

For team B, median = 8

Difference in medians = 8 - 4 = 4

The inrerquartile range is the difference between the third and first quartile. The third and first quartile are read from the graph as the two extreme points that serve as the beginning and end of the boxplot.

For team A, IQR = 5 - 2 = 3

For team B, IQR = 9 - 6 = 3

Since the two IQR are the same, we can easily adopt that the IQR = 3.

Hence, we can conclude that the difference in medians, 4, is (4/3) or 1.3333 times the IQR.

Hope this Helps!!!